Israelite is a term used to refer to people from the land of Israel, when talking about ancient and Biblical times. It usually refers to a member of one of the Twelve Tribes of Israel. The term Children of Israel is also used, especially when talking about the period of the Five Books of Moses. Now, a person from the modern State of Israel is called an Israeli.
Israelites lived in the kingdom of Israel, in areas where the country of Israel is now. Israel split off from a kingdom called Judah, whose people were later called Jews. Israel was conquered by the Assyrians in 721 BCE. Judah was conquered by the Babylonians in 586 BCE. Many Jews were taken away from Judah. When the Persians defeated the Babylonians they let the Jews return to rebuild the Jewish Temple in Jerusalem about 70 years later.